CHICAGO (CBS) — Answering Mayor Rahm Emanuel’s call to come up with $10 million in cost savings to avoid 625 layoffs, union leaders on Tuesday offered their own ideas to save nearly $250 million a year.

CBS 2 Chief Correspondent Jay Levine reports that labor leaders claim their report on how to save almost $250 million without laying off rank-and-file city workers is serious.

But $100 million of it is just a guess — the savings from what they call a “full performance review.”

The rest of it comes from some of the things Emanuel was already talking about, although in a slightly different way.

Last week, the mayor announced that he was outsourcing part of the city’s recycling program, saying it would provide “managed competition” between city workers and private businesses.

Emanuel said the move would save the city more than $3 million a year, but it’s a move labor leaders tried to portray as a bad financial deal for the city.

“We need to make sure managed competition is fair competition,” Chicago Federation of Labor President Jorge Ramirez said Tuesday.

The labor leaders did offer suggestions about more efficient ways of doing things. In some cases, they said four 10-hour days would be more productive than five 8-hour days. But they still disagreed on work rules.

For example, CBS 2 found a city crew – consisting of a supervisor, two truck drivers, two laborers, and three city vehicles – assigned to a small sidewalk job that even they seemed to think was a bit of a stretch.

“Alright, you guys get more work up for us,” one of the workers said.

Emanuel has complained about work rules that left workers sitting around and waiting.

But Ramirez said, “it’s our belief that before you go into negotiating work rule changes, or anything else, you should make sure that you’re managing things the way that they should be managed.”

For his part, the mayor said “any part of the budget, from the mayor’s office to work rule reforms and everything between those boundaries is not off limits, it’s on limits.”

Emanuel applauded cement masons who, as CBS 2 reported last night, agreed to work rule changes cutting overtime pay from double time to time-and-a-half. He said if all other unions followed suit, it would save $4 million and hundreds of jobs.

But even that’s small potatoes when it comes to the hundreds of millions in savings contained in labor’s consultants’ report, which you can bet the mayor’s people are going over with a fine tooth comb.

In a letter sent out to labor leaders Tuesday afternoon, Emanuel said, “I appreciate the effort made by the Chicago Federation of Labor in coming forward with today’s ideas. I will review the report with my team so that we can begin to discuss how to incorporate these and other ideas in a way that best serves the city’s taxpayers in 2012 and beyond.”

Emanuel said he has already taken action on some of the suggestions mentioned in the report, including cutting the mayor’s office payroll by 10 percent and cutting 100 non-union management positions. He also said he’s put a hiring freeze on an additional 175 management positions.

The mayor claimed those moves have saved the city $21 million.

“And my administration is not stopping there. As you know, I have instructed my cabinet to do a top-to-bottom review of each department to identify savings and deliver services more efficiently in the future,” Emanuel added. “No idea is too small and no area of government is immune from review or reform. As I said in my inaugural address, if we all give a little, no one will have to give too much. “

He also announced the formation of an “official working group” to focus on reforms that could save the city a minimum of $100 million. He’s appointed his deputy mayor, budget director and government affairs director to the team and has asked labor leaders to name a group of partners to team up with that group.